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## [Axiom-developer] Re: [Axiom-mail] beginner question about sum(...)

 From: Kostas Oikonomou Subject: [Axiom-developer] Re: [Axiom-mail] beginner question about sum(...) Date: Tue, 01 Feb 2005 09:01:44 -0500 User-agent: Opera M2/7.54 (SunOS, build 751)

```Hello Martin,

the sum
1/(k*(k+a)) is hypergeometric. And indeed Axiom evaluates it if you give "a" a
positive
integral value.  Now wouldn't you expect that if you declared "a" to be a
positive integer
the summation would be evaluated?  It is not.  Instead Axiom says that "a" has
not been
given a value.

situation.  That if
you make a certain type declaration, you would expect Axiom to act accordingly,
but it
does not appear to do so.

Regards,

Kostas

```
```Dear Kostas,

Kostas Oikonomou writes:
>
> But I was disappointed by the sum(1/k^2, k=1..n) example.  I saw that
> Gosper's method is implemented in sum.spad.pamphlet, but this (rather
> simple) sum needs symbolic manipulation of gamma and psi functions, which is
> not there.  More generally, special functions seem to be handled only
> numerically.  At least for my prospective use of Axiom, this points to a
> rather big "hole". And I wonder how many others of this sort there are.
>
> I also tried sum(1/(k*(k+a)), k=1..n).  That was also returned unevaluated,
> although Gosper's method should handle it.

Why should Gosper's method handle it? As far as I can see the solution is not
hypergeometric?

Martin

```
```

```